A ring R is called a strongly ur-clean ring, if every element x ∈ R can be expressed as x = a + e and ea = ae for a unit-regular element a and an idempotent element e. This article presents several properties of a strongly ur-clean ring, namely, if x is an element in a strongly ur-clean ring R, then the element (1 - x) ∈ R, properties of a strongly ur-clean ring on its factor ring, the eRe ring, the elemental characteristics of the Jacobson radical with its elements having special properties for a strongly ur-clean ring, and the unit element characteristics with special properties for a reduced strongly ur-clean ring. In addition, this article also presents the relationship between a strongly ur-clean ring and a strongly clean ring, as well as the properties of the elements of a strongly ur-clean ring to a strongly clean ring.
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2 November 2022
THE 2ND INTERNATIONAL CONFERENCE ON MATHEMATICS AND ITS APPLICATIONS (ICoMathApp) 2021: The Latest Trends and Opportunities on Mathematics' Research and its Applications
26–27 October 2021
Malang, Indonesia
Research Article|
November 02 2022
Strongly UR-Clean ring: Properties and relation to strongly clean ring
I Made Sulandra;
I Made Sulandra
a)
1
Universitas Negeri Malang
, Malang, Indonesia
a)Corresponding author: [email protected]
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a)Corresponding author: [email protected]
AIP Conf. Proc. 2639, 020001 (2022)
Citation
I Made Sulandra, Wiskandar; Strongly UR-Clean ring: Properties and relation to strongly clean ring. AIP Conf. Proc. 2 November 2022; 2639 (1): 020001. https://doi.org/10.1063/5.0110053
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